On the Arithmetic and Geometric Fusion of Beliefs for Distributed Inference

• 成果类型: Article
• 署名作者: Kayaalp, Mert; Inan, Yunus; Telatar, Emre; Sayed, Ali H.
• 署名单位: Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3330405
• 发表日期: 2024
• 页码: 2265-2280
• 关键词: Bayes methods; TOPOLOGY; testing; Peer-to-peer computing; Network topology; estimation; STANDARDS; Asymptotic decay rate; distributed decision-making; fusion of belief vectors; linear and logarithmic opinion pools; social learning

摘要

We study the asymptotic learning rates of belief vectors in a distributed hypothesis testing problem under linear and log-linear combination rules. We show that under both combination strategies, agents are able to learn the truth exponentially fast, with a faster rate under log-linear fusion. We examine the gap between the rates in terms of network connectivity and information diversity. We also provide closed-form expressions for special cases involving federated architectures and exchangeable networks.